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Digital Transmission of Analog Signals The Communications Edge™ Tech-note Author: John F. Delozier Digital Transmission of Analog Signals The digital transmission of analog information ment that is similar to the improvement is an old idea which has always had a certain V found when wideband FM systems are com- amount of appeal to telecommunication sys- τ pared to AM systems. (a) tem designers. If a minimum level of signal- T to-noise ratio is maintained, then it is possible DIGITAL PULSE MODULATION to operate a digital transmission system (b) Pulse code modulation (PCM) and delta almost error free. modulation (DM) are the major digital pulse It is the intent of this article to provide a brief formats. Digital pulse modulation is charac- tutorial on digital telecommunications for terized by the representation of the informa- personnel not already familiar with this sub- (c) tion signal as a discrete value in a finite set of ject. As background material, some modula- values. Pulse code modulation begins with a tion and multiplexing techniques will be cov- sampled information signal (PAM) whose sample amplitudes are quantized and encoded ered initially. The focus of the article will be a (d) UNMODULATED presentation of the two major telecommuni- PULSES into a finite number of bits or into an n-bit cation hierarchies found in today’s networks word. The implementation of PCM is more complicated than analog pulse modulation and then digital transmission via microwave (e) formats, but PCM’s transmission and regener- modulation techniques will be briefly covered. Figure 1. Pulse modulation format. The carrier pulse train ation capabilities are more attractive. The “a” can represent the analog signal “b” by continuous vari- sequence leading from an information signal ANALOG PULSE MODULATION ation of the pulse amplitude “c,” the pulse width “d,” or the pulse position “e.” to a PCM word is depicted in Figure 3. The The continuous variation of the amplitude, transmission and regeneration capabilities of width, or position of the pulses in a pulse sampling rate of 2B samples per second is PCM lie in the way in which information is train to represent an information signal is called the Nyquist sampling rate and 1/(2B) is carried in the presence (or absence) of pulses, defined as analog pulse modulation (examples called the Nyquist sampling interval. Figure 2 and not in the amplitude of the pulse or the are shown in Figure 1). The examples are, illustrates the sampling process. location of the edges of the pulse. Analog respectively, pulse amplitude modulation Analog pulse modulation is attractive for pulse modulation formats can withstand only (PAM), pulse width modulation (PWM) and many data-handling applications due to the a limited number of repeaters in a noisy sys- pulse position modulation (PPM). These ease with which it can be implemented. tem, while the PCM format is generally modulation formats were among the first of Analog pulse modulation is also attractive immune to system noise as long as the the pulse techniques to be utilized, and can because some modulation formats like PWM repeaters or regenerators are properly spaced. still be found in existing telecommunication and PPM show a signal-to-noise improve- The price paid for transmitting information and telemetry networks. But, more significant, almost noise-free lies in the quantization dis- is that PAM is utilized as the first step in tortion generated and the larger system band- many digital pulse modulation formats. f(t) widths required (as in wideband FM). Digital transmission is performed by discrete Delta modulation is a digital pulse modula- bundles of energy called pulses. The founda- τ tion technique which has found widespread tion for this concept arises out of the work T (a) t acceptance in the military sector because of done in sampling theory by Henry Nyquist of the requirements for low bit-rate digital sys- the Bell Telephone Laboratories. Briefly, fs(t) tems. Delta modulation is differential in Nyquist explained that if a signal, f(t), was nature; it transmits a signal which is related to bandlimited to B Hertz, then the signal could the difference between successive signal val- only change at a maximum rate of B Hertz. (b) t ues, as opposed to the actual value of the He further showed that if a sample of the information signal at a given time. The differ- Figure 2. The sampling process. The analog signal ft is band-limited signal is taken every 1/(2B) sec- sampled every T seconds for a time of τ seconds (a), ence signal, Vd(t) (shown in Figure 4), is onds, no information is lost. The minimum which generates the PAM signal (b). developed by comparing the value of the WJ Communications, Inc. • 401 River Oaks Parkway • San Jose, CA 95134-1918 • Phone: 1-800-WJ1-4401 • Fax: 408-577-6620 • e-mail: [email protected] • Web site: www.wj.com The Communications Edge™ Tech-note Author: John F. Delozier evident in the first two intervals of the wave- forms. The delta modulators in use today change (a) their step size in response to the steepness of the slope so that they can respond quickly to large dynamic changes in signal amplitude. Another attractive feature of the delta modu- lator is that the circuitry is easier to imple- ment than PCM circuitry. INCREASED UTILIZATION (b) THROUGH MULTIPLEXING One method for increasing the utilization of a communication channel is by sharing the channel among two or more signals. Sharing may be done on either a phase, frequency, or time basis, or combination thereof. Multiplexing is the sharing of a communications path among signals, and in telecommunications, the more commonly found multiplexing sys- tems are implemented on either a frequency (c) or a time basis. The sharing of a telecommunication channel on a frequency basis is called frequency divi- TYPES OF PULSE MODULATION: (a) MODULATING SIGNAL sion multiplex (FDM). Each signal is nomi- (b) PULSE-AMPLITUDE MODULATION nally 3 kHz in bandwidth and, in FDM, each (c) PULSE-CODE MODULATION signal is translated in frequency to any one of Figure 3. PCM word generation. The modulated signal (a) is sampled and produces a PAM signal (b). Each PAM pulse many pre-assigned spectral locations. is then coded into a PCM word (c). Translation is accomplished using single-side- input, Vin(t), with the estimate, Vi(t), of the input. The polarity of the difference signal at the band modulation (SSB) techniques because sampling instant determines the polarity of the pulse transmitted, Vout(t). The difference signal SSB format allows the signal to be transmit- is a measure of the slope of the signal. ted without a redundant signal (sideband) or a carrier. The first level of FDM will create a A delta modulator is shown in block diagram form in Figure 4. The pulse generator furnishes a composite signal containing twelve channels regularly recurring train of pulses, V (t), of fixed amplitude and polarity. To simplify the illustra- p that are designated as a group. Before trans- tion, the pulses are assumed to be impulses. The operation of the modulator may be seen using mission, groups are usually combined, using the waveforms of Figure 4. In this figure, t = 0 has been selected to occur at a pulse occurrence. FDM principles, into larger aggregates called The initial value of V (t) is 2 units and the initial value of V (t) is assumed to be 0. The polarity in i super groups, master groups, and super mas- of the difference signal is positive, and a positive impulse is transmitted. At the next sampling ter groups. At the receiving end, demultiplex- instant, T, the impulse is positive. At the sampling instant, 2T, the impulse is negative because ing is aided by the hierarchical structure and the integrated pulse is 2 units and the value of V (2T) is less than 2 units, which results in a in the presence of single-tone signals called pilot negative polarity for the difference signal. Examination of the waveforms of Figure 4 reveals two tones. points: (1) In the presence of zero slope, the modulator’s output is a pulse train of alternating polarity. Demodulation is accomplished by integration and low-pass filtering. The pulse train of Time division multiplex (TDM) in creases alternating polarity will integrate to its average value. If no signal is put in, then the pulse train the utilization of a telecommunication trans- will have an average value of zero. (2) The modulator cannot respond quickly to signals whose mission channel by sharing that channel amplitudes change by more than a unit step from one sampling instant to the next. This is among many signals on a time basis. If the WJ Communications, Inc. • 401 River Oaks Parkway • San Jose, CA 95134-1918 • Phone: 1-800-WJ1-4401 • e-mail: [email protected] • Web site: www.wj.com The Communications Edge™ Tech-note Author: John F. Delozier PULSE f(t) GENERATOR 1 τ < 2B DIFFERENCE VIN(t) SIGNAL ANALOG SIGNAL + Vd(t) VOUT(t) COMPARATOR MODULATOR - τ Vi(t) Vfeedback(t) INTEGRATOR 1 1 0 1 1 Vd(t) - VIN(t) - Vi(t) -- B 2B 2B B Vp(t) Figure 5. The sampling process. The duration τ is a por- 121 3456 78910111213141516 17 18 19 20 21 22 23 24 25 26 27 tion of the sampling interval (1/2B). t (TIME) width requirements forms the basis for the use of TDM in telecommunications. Vin(t) Three of the consequences of allowing the pulse duration to decrease are: (1) Wider transmission bandwidths; (2) Due to trans- mission bandwidths not being infinitely wide, pulse spreading occurs, which requires 2 that new pulses be regenerated regularly; (3) 1 Pulses must stay within certain time windows, Vi(t) which requires additional circuitry for syn- -1 chronization purposes.
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